* Put/call ratio below long-term average
* Europe's 'fear gauge' nears 2014 low, even after EM rout
* Investors complacent about possible market sell-offs
By Tricia Wright
LONDON, Feb 20 (Reuters) - European equity investors kept their nerve through an emerging- markets slump and are positioning for a rally in coming months, betting on an improving regional economy and support from central banks if things go wrong.
Markets lost ground on Thursday, held back by a contraction in China's factory activity and France's service sector, but investor sentiment is still broadly positive.
The euro zone blue-chip Euro STOXX 50 index has rebounded since it lost more than 7 percent in late January and early February, when declining emerging-market assets spooked investors. The index is now back within sight of last month's 5 1/2-year peaks.
Europe's equity funds are enjoying strong inflows, markets are not far from multi-year highs and volatility, a crude gauge of risk aversion based on how much investors are prepared to pay for options, is near its low for the year.
In recent months, investors have been buying fewer put options, which offer protection against market falls, on the blue-chips index than at any time over the past year, Eurex data show. That is despite sharp currency swings in emerging markets and signs of uneven economic recovery.
For every call option, which are bets on market gains, on the Euro STOXX 50, there are just 1.2 puts, just below the long-term average ratio. The ratio has gradually fallen from four to one in early October 2013, when investors were worried about the impact of an impending U.S. government shutdown, according to Thomson Reuters Datastream.
Ahead of Friday's expiration of European stock options, open interest on calls was heavier than on puts on the Eurex exchange.
"People are not ... that worried. It's not really about downside, it's about: is there more upside?" Vincent Cassot, head of equity derivatives research at Societe Generale Corporate & Investment Banking, said.
Eating into demand for puts is the fact that investors believe the region's economy is slowly on the mend, while the European Central Bank has kept interest rates at a record low and is ready to act if deflation threatens the recovery.
In a further sign of investors' appetite for European shares, the region's equity funds have seen record inflows this year, according to data from EPFR Global.
"Over time, you realise that put options don't really pay off that often, because every time there's a bit of a wobble, you get intervention by the central banks," said Kokou Agbo-Bloua, European head of equity and derivative strategy at BNP Paribas.